2013 jetta cigarette lighter fuse location Mk6 Diagram VW Golf Mk7 Fuse Box
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I just went out and checked after reading your post and when I turn on the blower fan, to any setting, I get no fan power at all so I guess my car is wired differently from yours somehow
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#11 azthegame: could be a bad relay but we did this same mod in 2 cars (a 2012 and 2013), both behave the same way

Test the fuse with your multimeter, then try out the lighter socket

[4] If the panel doesnt contain a removal tool, use household tweezers or needle-nose pliers from your toolbox

[14] Video Tips Keep the socket covered with its plastic cap, or keep the lighter plug inserted in the socket, when youre not using it